pdf f(x)=1/(x*S*sqrt(2*pie))*integral exp(-((lnx)-m)^2/(2*S^2))dx
mean=integral((f(x).x.)dx /*x will cancel up in this case)
mean= integral(1/(S*sqrt(2*pie)*exp(-((lnx)-m)^2/(2*S^2))dx
solving as you discuseed by assuming ln(x)=y we get
integral(1/(S*sqrt(2*pie)*exp(-(y-m)^2/(2*S^2))*...